The statement "The charge without mass is not possible" is correct based on our current understanding of physics because:

• All known charged particles, such as electrons, protons, and ions, have mass associated with them. There is no experimental evidence of a physical entity that carries charge but has zero mass.
• Even in the case of hypothetical particles like the photon, which is massless, it does not carry electric charge. Charged particles inherently possess mass due to their nature in both classical and quantum physics.

Thus, charge is always associated with some mass in all observed phenomena.

The relativistic formula for mass,

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

accounts for how mass increases with velocity. This behavior arises because mass is a form of energy, and energy is affected by motion under relativity.

However, electric charge (

$q$

) is invariant under relativistic mechanics. Charge does not depend on the velocity of the particle. It remains constant in all inertial reference frames, which is a fundamental principle in physics.

Thus, the equivalent relation for electric charge is simply:

$$q = q_0$$

This reflects the fact that charge does not vary with velocity, unlike mass.

Here’s the reasoning behind the incorrect statements A and C:

(A) Incorrect:

• In frictional charging, the body with a lower work function (which requires less energy to remove electrons) will lose electrons and acquire a positive charge, while the one with a higher work function will gain electrons and acquire a negative charge. Thus, the statement is reversed.

(C) Incorrect:

• In induction, the inducing body does not get an opposite charge. Instead, the induced charge on the other body is opposite in nature to the inducing charge, while the inducing body retains its original charge. Therefore, this statement is wrong.

Additional Notes:

• (B) Correct: In conduction, charge transfer continues until both bodies achieve the same potential.
• (D) Correct: Induction involves the rearrangement of charges within a body due to the presence of a nearby charged object. It is a property of the body itself.

Charging a body positively involves removing electrons. Since electrons have mass, removing them decreases the body's mass. Thus, both statements are true and Reason is the correct explanation.

A matches with S (inverse square law), B with P (charge/area), C with R (\(q=ne\)), and D with Q (flux).

Using quantization of charge, \(q = ne ⇒ n = \frac{q}{e} = \frac{10^{-10}}{1.6 \times 10^{-19}} = 6.25 \times 10^8\).

When a neutral body is charged positively, it loses electrons. Since electrons have a finite mass \((m_e \approx 9.1 \times 10^{-31}\text{ kg})\), the loss of electrons results in a slight decrease in its mass and weight.

By quantization of charge, \(q = ne\). Solving for \(n\), we get \(n = \frac{q}{e} = \frac{10^{-10}\text{ C}}{1.6 \times 10^{-19}\text{ C}} = 6.25 \times 10^8\).

Assertion (A) is true: Aircraft tyres are made slightly conducting to discharge static electricity accumulated during flight.nReason (R) is true: Grounding allows excess charge to flow to Earth.

(R) correctly explains (A) as the purpose of conducting tyres is to discharge static charge to the ground safely.

Assertion (A) is true, considering 'mass' as rest mass, which is invariant, similar to charge. Reason (R) is true: All charged particles possess mass; a massless particle cannot carry charge.

(R) is not the correct explanation for (A), as invariance of charge and rest mass are fundamental properties, not directly explained by their association.